Hanging Cantilever Load Calculator

Cantilever Deflection Formula:

\[ \delta = \frac{W \cdot L^3}{3 \cdot E \cdot I} \]

Load (W):

Length (L):

Modulus (E):

Inertia (I):

m⁴

Deflection (δ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Cantilever Deflection Formula?

The cantilever deflection formula calculates the maximum deflection of a cantilever beam with a point load at the free end. This is a fundamental equation in structural engineering used to determine how much a beam will bend under a specific load.

2. How Does the Calculator Work?

The calculator uses the cantilever deflection formula:

\[ \delta = \frac{W \cdot L^3}{3 \cdot E \cdot I} \]

Where:

\( W \) — Applied load (N)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)
\( \delta \) — Maximum deflection (m)

Explanation: The formula shows that deflection increases with the cube of the beam length and is inversely proportional to both the modulus of elasticity and moment of inertia.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to ensure that beams and cantilevers don't deflect beyond acceptable limits, which could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter all values in the specified units. Load (W) in Newtons, length (L) in meters, modulus (E) in Pascals, and inertia (I) in meters to the fourth power. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a rigid structural element that extends horizontally and is supported at only one end.

Q2: When is this formula applicable?
A: This formula applies to cantilever beams with a point load at the free end and assumes linear elastic material behavior and small deflections.

Q3: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Wood: ~10 GPa (varies by species and direction).

Q4: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For rectangular sections: I = (b·h³)/12, where b is width and h is height.

Q5: What are deflection limits in structural design?
A: Deflection limits vary by application but are typically L/360 for live loads and L/240 for total loads in building design, where L is the span length.